The formidable campaign apparatus that has sprung up to support a possible 2016 presidential bid by Hillary Clinton is rattling some Democrats, sparking concerns that it could suppress competition for the party nomination and siphon money from candidates running in the midterm elections this fall.

With Democrats fighting to keep control of the Senate in the midterms, the emergence of the pro-Clinton super PAC Priorities USA could eat into donations that the party's candidates need to win in November, some Democrats warn....